My current project calls for me to render a white square with the edges a separate color. We will use black for the purpose of this exercise. How would I go about rending the edges of a polygon object black, while the faces are white?

If you're rendering with Arnold, you can do it super easily with a aiWireframe node, and play with fill and line colors,

If you're rendering with Mental Ray you need to apply a material to your objects, then go on the shadingGroup of the assigned material, while Mental Ray is your current renderer go in the mental ray tab of your shadingGroup then you have a Contours section, turn on Enable Contour Rendering then play with values, if you want a flat cube you can just assign a simple surfaceShader (right click -> assign Favorite Material -> Surface Shader)